Code to reproduce the results for https://arxiv.org/abs/2308.05657

Numeric integration of arbitrary functions using quantum machine learning

This project implements the ideas of 2211.02834 in quantum circuits exploting the implementation of the VQE and the Parameter Shift Rule available in qibo

The code is based on the main.py script and a list of utilities in the qinntegrate folder. It is not a library but rather a collection of scripts that uses the Qibo library underneath which does all the heavy (quantum) lifting.

  python main.py --help

usage: main.py [-h] [--xmin XMIN [XMIN ...]] [--xmax XMAX [XMAX ...]] [-o OUTPUT] [-l LOAD] [-j JOBS]
            [--target TARGET] [--parameters PARAMETERS [PARAMETERS ...]] [--ndim NDIM] [--ansatz ANSATZ]
            [--nqubits NQUBITS] [--layers LAYERS] [--nshots NSHOTS] [--pdf_alpha PDF_ALPHA] [--maxiter MAXITER]
            [--npoints NPOINTS] [--padding] [--absolute] [--optimizer OPTIMIZER] [--nruns NRUNS]

options:
  -h, --help            show this help message and exit
  --xmin XMIN [XMIN ...]
                        Integration limit xi
  --xmax XMAX [XMAX ...]
                        Integration limit xf
  -o OUTPUT, --output OUTPUT
                        Output folder
  -l LOAD, --load LOAD  Load initial parameters from
  -j JOBS, --jobs JOBS  Number of processes to utilize (default 4)

Target function:
  --target TARGET       Select target function, available:
                  ['sin1d', 'cosnd', 'sind', 'lepage', 'uquark', 'uquark2d', 'cosndalpha', 'toy']
  --parameters PARAMETERS [PARAMETERS ...]
                        List of parameters for the target functions
  --ndim NDIM           Number of dimensions

Circuit definition:
  --ansatz ANSATZ       Circuit ansatz, please choose one among
                      ['base', 'reuploading', 'deepup', 'verticup', 'qpdf', 'qpdf2q', 'goodscaling']
  --nqubits NQUBITS     Number of qubits for the VQE
  --layers LAYERS       Number of layers for the VQE
  --nshots NSHOTS       Number of shots for each < Z > evaluation
  --pdf_alpha PDF_ALPHA
                        (only value for PDF ansatzs) value of alpha in the PDF prefactor

Optimization definition:
  --maxiter MAXITER     Maximum number of iterations (default 1000)
  --npoints NPOINTS     Training points (default 500)
  --padding             Train the function beyond the integration limits
  --absolute            Don't normalize MSE by the size of the integrand
  --optimizer OPTIMIZER Optimizers, available options:
                           ['cma', 'bfgs', 'sgd', 'lbfgs', 'annealing', 'basinhopping']
  --nruns NRUNS         Number of times the optimization is repeated

Some example commands:

python main.py --parameters 1 2 3  --optimizer lbfgs --absolute --layers 2 --nqubits 2 -j 18 --ndim 4 --target toy --ansatz goodscaling --maxiter 200 -o output_folder
python main.py --optimizer lbfgs --absolute --npoints 100 --layers 2 --nqubits 2 --ndim 4 --target cosnd --ansatz goodscaling -j 16
python main.py --optimizer cma --npoints 50 --layers 1 --absolute --nqubits 1 --ndim 1 --nshots 1000 --target sin1d --ansatz deepup -j 8